Kerala Board Class 10 Mathematics — Flashcards for Quick Revision

A: Division Algorithm: Given positive integers a and b, there exist unique whole numbers q and r such that a = bq + r, where 0 ≤ r < b. Here, a is dividend, b is divisor, q is quotient, and r is remainde

A: Euclid's Algorithm is a technique to find HCF of two given integers. Steps: 1) Apply division algorithm to larger and smaller number 2) If remainder = 0, divisor is HCF 3) If remainder ≠ 0, apply divi

A: Step 1: 100 = 60 × 1 + 40 Step 2: 60 = 40 × 1 + 20 Step 3: 40 = 20 × 2 + 0 Since remainder is 0, HCF(60, 100) = 20

A: A set is a well-defined collection of distinct objects. The objects in a set are called elements. Sets are written by enclosing all elements between brackets { }. Example: Set of first five prime num

A: 1. Roster Form (Listing Form): Elements are listed within curly brackets Example: A = {2, 4, 6, 8, 10} 2. Set-builder Form: Elements are defined by a common property Example: A = {x : x is an e

A: • ∈ (belongs to): Used when an element is in the set Example: 5 ∈ {1, 3, 5, 7, 9} • ∉ (does not belong to): Used when an element is not in the set Example: 6 ∉ {1, 3, 5, 7, 9}

A: A polynomial in x is an algebraic expression containing the sum of a finite number of terms of the form ax^n, where 'a' is a real number, a ≠ 0, and 'n' is a whole number. Example: 3x² + 5x - 2

A: Linear polynomial: degree 1 (e.g., 3x + 5) Quadratic polynomial: degree 2 (e.g., x² + 5x + 4) Cubic polynomial: degree 3 (e.g., 2x³ - 4x² + x - 1)

A: The degree of a polynomial p(x) is the highest power of x in p(x). For example, in 5x³ - 4x² + x - 1, the degree is 3.